Understanding Global Warming: How to Build a Greenhouse Effect

All of us have heard something about global warming in the media, or perhaps in documentaries such as Al Gore´s Inconvenient Truth. Any good Weather and Climate blog should have something that talks about the science of climate change, and the facts vs. fiction of what gets spread around in popular discussions. Most of my future posts will be geared toward this theme, and this one will start with some of the basics: understanding the greenhouse effect, and how it can raise Earth´s temperature.

It must be mentioned that the greenhouse effect is something natural to Earth´s atmosphere, and even to the atmospheres of other planets. When you hear people talking about humans increasing the temperature of Earth, the idea is what we are making the greenhouse effect stronger. We are doing this by putting more greenhouse gases in the atmosphere. How does this all work?

As we all know, the Earth absorbs large amounts of energy from the sun. In fact, over every square meter, Earth absorbs sunlight at a higher rate than any other body with an atmosphere in our solar system. The amount of solar energy powering the Earth is about 122 million billion Watts. This is more than 100 million times the power from a typical electrical power plant. Meanwhile, a typical light bulb might be rated at something close to 100 Watts. The energy from the sun dominates any other source of energy and is what drives the weather and life as we know it.

We also know that the Earth does not continue to build up energy from the sun and continue to get hotter and hotter forever. This is because the Earth is also releasing its own energy out into outer space. When this energy leaks away, the Earth cools off. Eventually the Earth reaches an equilibrium point when the amount of sunlight it absorbs equals the amount of energy it sheds into space.

The energy Earth releases is called infrared radiation, and humans don´t see this type of ¨light¨ but we can feel it as heat off of nearby objects. If we could see infrared energy, it would appear just beyond the red side of a rainbow. Infrared is a different sort of ¨light¨ than we see from the sun, which is primarily visible light (for obvious reasons). It also happens that certain gases in our atmosphere interact with infrared radiation much more than they do sunlight. These are so-called greenhouse gases.

One of my favorite definitions of a greenhouse gas is actually intended to be humorous

Greenhouse gases: Any gas that, by an accident of chemistry, happens to absorb radiation of a type that the Earth, by an accident of history, would like to lose. (from Gavin Schmidt and Joshua Wolfe- Climate Change: Picturing the Science)

One of the fundamental physics problems that atmospheric science undergraduates will work out sometime in their schooling is determining what Earth´s temperature would be without an atmosphere. There are some assumptions involved in this problem, but averaged over the globe, the Earth would be below freezing. The oceans would become ice-covered and the Earth uninhabitable. The Earth is at least 60 degrees Fahrenheit warmer than this hypothetical scenario due to greenhouse gases.

Most of our atmosphere is composed of nitrogen and oxygen. They make up well over 95% of our atmosphere, except in the very moist tropics, where water vapor can make up a few percent of the local air. These gases helps us breathe, but on their own, they would not change the temperature much. They are not greenhouse gases because they do not interact with infrared radiation, at least not at pressures or temperatures of any concern to us on Earth.

In contrast, a very small amount of our atmosphere is composed of water vapor, carbon dioxide (CO2), methane, (CH4), ozone (O3), and some other more complex molecules. These gases have the chemical properties allowing them to interact strongly with Earth´s infrared radiation, absorbing it and delaying its exit to outer space. As trivia, see if you can spot what might be different about these molecules, as compared to oxygen and nitrogen (O2 and N2). We can talk about this in the comments.

The greenhouse effect works when these gases reduce how efficiently the Earth loses its flow of energy. That increases the temperature of the surface. The way that works is similar to the way adding fiberglass insulation windows to your home increases its temperature, even though you do not need additional energy coming from the furnace. Some people do not like this analogy because houses and greenhouses lose a lot of energy by warm air moving away- that is, by turbulent ¨convection¨- meanwhile the Earth loses energy by infrared radiation. In the end, however, CO2 and other greenhouse gases are just planetary insulation.

In the 1800´s, physicist John Tyndall used a brilliant analogy to describe this effect:

“As a dam built across a river causes a local deepening of the stream, so our atmosphere, thrown as a barrier across the terrestrial rays, produces a local heightening of the temperature at the Earth’s surface.”

In fact, this analogy is adequate. Adding more and more greenhouse gases causes Earth´s outgoing energy to have a more difficult time escaping into space; as a consequence, energy cannot escape from the Earth until it reaches the thin upper atmosphere. This makes the heat loss more ¨sluggish¨ and makes the surface hotter and hotter.

Our sister planet, Venus, is an example of a much more intense greenhouse effect. Venus´ atmosphere is composed almost entirely of carbon dioxide, and also small amounts of water vapor and sulfur dioxide. It generates more than 90 times the pressure on the surface as does Earth´s atmosphere, almost the same pressure you would experience swimming half a mile under the ocean! This is more than enough to crush a human.

As a consequence of its thicker greenhouse atmosphere, Venus is the home to the strongest greenhouse effect in the solar system, keeping the planet at a not-too-comfortable 860 degrees Fahrenheit! This temperature can melt lead or tin, and is even hotter than Mercury, which is closer the sun!

Compare Earth with Venus on the left, noting how much harder it is for energy leaving the planet to escape Venus, and can only do so in the very high atmosphere where it is thin and cold. Red arrows represent the emission of infrared radiation outward to space. Note also that some energy will be radiated back to the surface.

So, if someone at a party asks you how more CO2 in the atmosphere causes global warming, you can tell them it is because it traps Earth´s heat, making it more difficult for the planet to cool off. More precisely, for the same temperature, Earth´s total outgoing energy is reduced while the incoming energy from the sun stays the same; the result is that the Earth wants to warm up, so it can come back into a new equilibrium.

Good question. Actually, Venus is closer to the sun, but it *absorbs* much less sunlight than the Earth does. This is because it has several layers of thick clouds made of sulfuric acid…these clouds end up reflecting about 75% of all the solar energy right back out into space. That reflected energy is irrelevant for heating the planet. Earth only reflects about 30% of its total incoming sunlight away.

That difference actually over-compensates for the closer distance to the sun, so everything else staying the same, less sunlight is available to heat Venus. I had this in mind when I said ¨In fact, over every square meter, Earth absorbs sunlight at a higher rate than any other body with an atmosphere in our solar system.¨

Now, what if Venus reflected the same amount of energy that Earth does? We can make that comparison so that the ONLY difference is the distance from the sun, and we compare them side by side.

In this case, I just did a quick calculation, and Venus´ no-atmosphere temperature would be about 80 degrees Fahrenheit, globally averaged. If Venus absorbed ALL of its incoming solar energy, that goes up to about 130 F. That is hotter than Earth, but nowhere near 860 F. And as I said, Venus is even hotter than Mercury.

I am going to temporarily hold off on your second question, because it is a bit more open-ended and I want to see if I can encourage a discussion. I will let you know what I think depending on where other comments may lead (if anyone responds at all).

As for your first question…

For every doubling of carbon dioxide, the reduction in outgoing energy is about 4 Watts over every square meter of the planet. It is a bit different over the tropics or Antarctica, but that is a good average ( measured near the top of the atmosphere).

CO2 concentrations are currently just short of 400 parts per million in the atmosphere (i.e., if you plucked a million molecules from the air, you would on average find 400 that were CO2; it is small number but very important for the flow of energy out of the planet), so if you move to 800 parts per million, that is the reduction in energy loss you get.

Note that the equations which determine this are not linear, which means that going from 400 to 500 parts per million produces a slightly larger effect than going from 500 to 600 parts per million. This is important! It turns out every doubling produces roughly the same change.

As far as what this all actually means for temperature, this is a huge question, and one I am going to spend a lot of time on in the future. For now, I will just say that there is no simple theoretical answer, and it depends on how a lot of things respond to that CO2 increase. But there are constraints from past climate studies and observations for what to expect. Keep posted…I will get to that topic eventually!

I have for several years been concerned about the possibilty that Photo-Voltaic power adopted on a significant scale would yield a non-trivial decrease in overall albedo, thus countering the impact of any reduction in CO2 emissions.

The statement “Earth only reflects about 30% of its total incoming sunlight away.” in your answer to Sylvain would appear to at least reduce this concern. Any thoughts?

Any such decrease in planetary albedo would be negligible on a global scale, and certainly much smaller than the reduction in radiative forcing by leveling off CO2. Ray Pierrehumbert, a climate scientist in Chicago, did a crude discussion of the impact on energy balance with the solar panel stuff here (with a bit of arithmetic too).

(Also, I´m not well informed on the alternative energy topic, but I do not gather anyone thinks large scale solar energy is going to be a serious fossil fuel replacement)

The only thing I can guess about your trivia question is that the molecules other than O and N have 3 or more atoms in the molecule. If I understand your post correctly, an increase in greenhouse gases would increase pressure as happens on Venus. Do you know if the average pressures have been increasing around the world? I thought your post was great!

Good answer! The details of all of this are heavy on chemistry and quantum physics, but briefly:

There needs to be some induced ¨asymmetry¨ in the molecule when it absorbs infrared radiation. Molecules like H2O have that asymmetry permanently. CO2 is normally symmetric, with two oxygen atoms hanging on either side of a carbon atom, but it can bend and have an asymmetric stretch as well; when these gases absorb intercept at just the right frequency, it can be absorbed.

Two-atom molecules (with the same atoms) like O2 and N2 cannot get that asymmetry, and there is no unequal sharing of electrons between one N atom and the other, and are thus inactive at absorbing infrared radiation. If you have a two-atom molecule like Nitric oxide, or NO (an ingredient for producing urban smog) those can become good greenhouse gases, but there is no example of one on Earth that is important.

On very dense atmosphere gases like H2 or N2 could become good greenhouse gases, since very frequent collisions end up making them act like something of a four-atom molecule that can absorb light. This effect works better in colder atmospheres too, so it is important on Jupiter, or even Saturn´s moon.

As far as your last question, the pressure is determined by the weight exerted by the overhead atmosphere you are standing under, which depends on all the molecules in the air, what they are, and the surface area they are spread over…it also depends on the planets gravity too. You could increase the pressure by injecting a lot more N2 into the atmosphere for example. CO2 is only a very small part of the atmosphere, and when we burn fossil fuels to make it, we´re also taking some oxygen out of the atmosphere too (which is not a big deal because there is so much of it) but the impact on total atmospheric pressure is negligible.

With respect to IR absorption. Your references to the asymmetry (or symmetry) of an absorber are correct. Let me add a little more information. All molecules vibrate (unless you are at absolute zero). The strength of the bond between atoms and the mass of the atoms dictate how much energy is needed to vibrate between two atoms either as a diatom or a molecule, this can be simply illustrated by the harmonic oscillator model. The reason a homonuclear diatom such as N2 or O2 does not absorb radiation is that there has to be an oscillating dipole moment between the atoms. As you pointed out with the unequal sharing of electrons (dipole), a homonuclear diatom has no dipole moment and thus no oscillating dipole (the electrons are shared equally between the two atoms). It is the oscillating dipole moment between two atoms that allows the resonant IR frequency to interact with the vibrating diatom and absorb.

The symmetry aspect dictates the “rules” for what vibrating modes are ‘active’ or ‘inactive’. For a linear molecule, such as CO2, the symmetric stretches, i.e. both oxygen atoms vibrating about the carbon symmetrically (imagine your fists being oxygen atoms and your head the carbon and you pump you arms in and out together) are ‘inactive’ again, because the symmetry cancels the oscillating dipole moments. While the asymmetric stretching modes are ‘active’, which is one of the absorption modes. The bending mode is also ‘active’. Group theory is used to determine a molecules symmetry and in general, the more symmetric a molecule is the fewer ‘active’ modes will be allowed for absorption.

Finally, rotation of the molecule also affects the frequency. As the molecule rotates at different quantum levels it couples with the vibrational mode, this branches the vibrational mode and broadens the spectral area in which it absorbs. The most classic example of this is the vibrational-rotational spectrum of HCl, often studied in P-Chem (at least we studied it when I was in school).

Do N2 and O2 not emit radiation? You say they do not absorb radiation, is this IR radiation or Radiation in general.

It seems that all matter above 0K emits radiation and if it emits then it absorbs, Chris calls this the Fruit Loop Effect, but you can Find+Replace and put anything you desire like “Greenhouse” Effect for example which is quite popular these days.

Chris, not a personal attack, simply clarifying the point that it is misleading to use similes when a proper understanding/description is available.

John, My question is not trivial as it has implications quite close to the surface.

John:
N2 and O2 do absorb and emit _some_ radiation. But it is very particular radiation. Namely, lines in the Ultraviolet and Visible. Plus a tiny amount of microwave. For looking at a greenhouse effect, we look at gases that can absorb radiation that the infrared radiation that the earth emits. N2 and O2 don’t do that. (Nor does Ar, the third major gas in the earth’s atmosphere.)

A nice introduction to radiative transfer is Grant Petty’s _A First Course in Atmospheric Radiation_, where you can get full details on which parts of the spectrum N2, O2, Ar absorb, and the contrast with CO2, N2O, CH4, and so forth.

Chris, et al.: can you shed some light on why Mars, whose atmosphere is over 95% CO2, does not have a runaway greenhouse effect a la Venus? Is it due to its greater distance from the sun? Or its very thin atmosphere (so even though it is mostly CO2, the volume of CO2 is insufficient to warm the surface)? Or both/combination/neither?

Less sunlight helps of course, but it is mostly the lack of atmosphere that forbids a strong greenhouse effect. The surface pressure on Mars is something closer to 10 millibars than it is 1000 mb on Earth. And actually, it gets cold enough (locally) on Mars for CO2 to condense out; every Martian year, about 30% of the CO2 atmosphere snows out in the polar caps of each hemisphere during their respective polar nights.

But even with 95% CO2 (and actually it still has much more CO2 per square meter than Earth), you need to have enough pressure to broaden the absorption lines of the greenhouse gases. The lack of anything else weakens absorption so much that the Martian CO2 ditch (the amount of energy absorbed that would otherwise escape to space) has a width somewhat less than Earth’s. If you introduced a 1 bar N2 atmosphere on Mars it could get warmer. The other problem for Mars is the lack of water vapor, which really helps give you a strong greenhouse effect.

By the way, despite hype often given in the media (or discussed in connection with Venus), the runaway greenhouse is not so much about CO2 as it is water. The CO2 atmsophere on Venus maintains high temperatures now, but it is somewhat of the end product of the runaway, rather than being in a runaway today; I talked about this a bit in my most recent post, but I should elaborate.

As you know, the amount of water vapor that can build up in Earth´s atmosphere is capped by the point it reaches saturation (the Clausius-Clapeyron equation). This is an exponential dependent function on temperature, so in a warmer atmosphere, you can support more water vapor. But water vapor also generates a greenhouse effect, making it warmer. This is a typical positive feedback, but unlike on Earth, it is possible to get to the point where the temperature continues to increase faster than you reach the saturation point. The optical depth is also related to the column of water vapor, so it is possible to calculate that as you keep this feedback going, eventually the outgoing radiation by the planet asymptotes to a fixed value. That is, the energy loss becomes independent of the surface temperature. Most studies have that value at ~310 W/m2. The current absorbed solar radiation is 240 W/m2 and Earth must lose that much to reach equilibrium. But say you dialed up the amount of sun the Earth receives, so it absorbed 350 W/m2. It is now taking in more radiation than Earth can ever emit, and the end result is that it never reaches equilibrium, and in fact continues to warm until eventually you reach the critical point on a phase diagram and you cannot possibly have liquid water. That is the runaway greenhouse, and you can reach equilibrium again once the oceans are gone. Depending on the size of the ocean, you might end up somewhere at a few thousand degrees K, and once you put this much water in the atmosphere it pretty much dilutes anything (so the runaway is actually pretty insensitive to the CO2, you just need a high enough solar absorption to sustain it). After this point, a lot of water will be lost to space since it reaches high enough in the air to be exposed to high intensity radiation, breaking up the hydrogen and dehydrating the planet forever.

The reason Venus ended up with its 90 bar CO2 atmosphere is (in principle) the aftermath of something like this, and has to do with the weathering chemistry I discussed in my most recent post ¨Causes and Timescales.¨ Once you have no liquid water, this feedback goes away, so there is no way to draw down CO2 into rocks; at the same time, it is still being released to the atmosphere volcanically. Earth has roughly the same amount of CO2 as Venus, but in our case it is almost all in the ground. With Venus, it can´t get in the ground.

So which is it? If “greenhouse gasses” in the atmosphere act as an insulation, why does it only work for outbound energy? Why is the incoming energy allowed to enter the system but not allowed to radiate? If the “greenhouse gasses” reflect the energy, they would cool the earth because the source is external to the system and more would be reflected away. If the “greenhouse gasses” absorb the energy, they exist closer to the vacuum of space (the heat sink) and would radiate that energy away from the earth more easily than if that energy was absorbed by the surface of the planet. Since the atmosphere is cooler as you ascend, it cannot be a source of heat to the surface (heat does not flow down from cool to hot).
The reason a greenhouse works is because of the ceiling. The Earth does not have a physical ceiling . . . in fact, it’s completely the opposite. The density of the atmosphere gets lower as you approach space until it finally transitions to a vacuum. The clear material not only traps gasses in a way that a planet cannot, it also heats up and can act as an additional source of energy to the system, something a vacuum cannot do.

Heat does radiate from cold to hot all the time…a photon from a cold object does not “see” a hot object and decide to turn around in the other direction. The net heat flow is from hot to cold however, as mandated by the laws of thermodynamics.

As far as what GHG’s absorb, it has nothing to do with whether radiation is incoming or outgoing as much as it has to do with the spectral selectivity of gases (involving allowed quantum energy transitions). They don’t interact much with visible light (although note that the atmosphere *does* absorb about 20% of the incoming energy), but rather is much more opaque in the longwave far-IR spectrum. If Earth were hot enough to emit visible outgoing radiation, the atmosphere would be pretty transparent to the outgoing flux.

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